LEADER 04920nam 2200721Ia 450 001 9910826713703321 005 20230607222204.0 010 $a1-281-95622-8 010 $a9786611956226 010 $a981-281-054-4 035 $a(CKB)1000000000538091 035 $a(EBL)1679503 035 $a(OCoLC)879074242 035 $a(SSID)ssj0000170956 035 $a(PQKBManifestationID)11155899 035 $a(PQKBTitleCode)TC0000170956 035 $a(PQKBWorkID)10235853 035 $a(PQKB)11276576 035 $a(MiAaPQ)EBC1679503 035 $a(WSP)00004494 035 $a(Au-PeEL)EBL1679503 035 $a(CaPaEBR)ebr10255985 035 $a(CaONFJC)MIL195622 035 $a(EXLCZ)991000000000538091 100 $a20001101d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aHigh-dimensional nonlinear diffusion stochastic processes$b[electronic resource] $emodelling for engineering applications /$fYevgeny Mamontov, Magnus Willander 210 $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$d2001 215 $a1 online resource (322 p.) 225 1 $aSeries on advances in mathematics for applied sciences ;$v56 300 $aDescription based upon print version of record. 311 $a981-02-4385-5 320 $aIncludes bibliographical references and index. 327 $aContents ; Preface ; Chapter 1 Introductory Chapter ; 1.1 Prerequisites for Reading ; 1.2 Random Variable. Stochastic Process. Random Field. High-Dimensional Process. One-Point Process 327 $a1.3 Two-Point Process. Expectation. Markov Process. Example of Non-Markov Process Associated with Multidimensional Markov Process 1.4 Preceding Subsequent and Transition Probability Densities. The Chapman-Kolmogorov Equation. Initial Condition for Markov Process 327 $a1.4.1 The Chapman-Kolmogorov equation 1.4.2 Initial condition for Markov process ; 1.5 Homogeneous Markov Process. Example of Markov Process: The Wiener Process ; 1.6 Expectation Variance and Standard Deviations of Markov Process 327 $a1.7 Invariant and Stationary Markov Processes. Covariance. Spectral Densities 1.8 Diffusion Process ; 1.9 Example of Diffusion Processes: Solutions of Ito's Stochastic Ordinary Differential Equation ; 1.10 The Kolmogorov Backward Equation 327 $a1.11 Figures of Merit. Diffusion Modelling of High-Dimensional Systems 1.12 Common Analytical Techniques to Determine Probability Densities of Diffusion Processes. The Kolmogorov Forward Equation ; 1.12.1 Probability density ; 1.12.2 Invariant probability density 327 $a1.12.3 Stationary probability density 330 $a This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs). The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficie 410 0$aSeries on advances in mathematics for applied sciences ;$v56. 606 $aEngineering$xMathematical models 606 $aStochastic processes 606 $aDiffusion processes 606 $aDifferential equations, Nonlinear 615 0$aEngineering$xMathematical models. 615 0$aStochastic processes. 615 0$aDiffusion processes. 615 0$aDifferential equations, Nonlinear. 676 $a519.23 700 $aMamontov$b Yevgeny$f1955-$01682624 701 $aWillander$b M$0724746 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910826713703321 996 $aHigh-dimensional nonlinear diffusion stochastic processes$94052886 997 $aUNINA